1# Data file for mpc_sqrt. 2# 3# Copyright (C) 2008, 2010, 2022 INRIA 4# 5# This file is part of GNU MPC. 6# 7# GNU MPC is free software; you can redistribute it and/or modify it under 8# the terms of the GNU Lesser General Public License as published by the 9# Free Software Foundation; either version 3 of the License, or (at your 10#o ption) any later version. 11# 12# GNU MPC is distributed in the hope that it will be useful, but WITHOUT ANY 13# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS 14# FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for 15# more details. 16# 17# You should have received a copy of the GNU Lesser General Public License 18# along with this program. If not, see http://www.gnu.org/licenses/ . 19# 20# The line format respects the parameter order in function prototype as 21# follow: 22# 23# INEX_RE INEX_IM PREC_ROP_RE ROP_RE PREC_ROP_IM ROP_IM PREC_OP_RE OP_RE PREC_OP_IM OP_IM RND_RE RND_IM 24# 25# see sin.dat for precisions 26 27# special values (following ISO C99 standard) 280 0 53 +inf 53 -inf 53 -inf 53 -inf N N 290 0 53 +0 53 -inf 53 -inf 53 -1 N N 300 0 53 +0 53 -inf 53 -inf 53 -0 N N 310 0 53 +0 53 +inf 53 -inf 53 +0 N N 320 0 53 +0 53 +inf 53 -inf 53 +1 N N 330 0 53 +inf 53 +inf 53 -inf 53 +inf N N 340 0 53 nan 53 inf 53 -inf 53 nan N N 350 0 53 +inf 53 -inf 53 -1 53 -inf N N 360 0 53 +0 53 -1 53 -1 53 -0 N N 370 0 53 +0 53 +1 53 -1 53 +0 N N 380 0 53 +inf 53 +inf 53 -1 53 +inf N N 390 0 53 nan 53 nan 53 -1 53 nan N N 400 0 53 +inf 53 -inf 53 -0 53 -inf N N 410 0 53 +1 53 -1 53 -0 53 -2 N N 420 0 53 +0 53 -0 53 -0 53 -0 N N 430 0 53 +0 53 +0 53 -0 53 +0 N N 440 0 53 +1 53 +1 53 -0 53 +2 N N 450 0 53 +inf 53 +inf 53 -0 53 +inf N N 460 0 53 nan 53 nan 53 -0 53 nan N N 470 0 53 +inf 53 -inf 53 +0 53 -inf N N 480 0 53 +1 53 -1 53 +0 53 -2 N N 490 0 53 +0 53 -0 53 +0 53 -0 N N 500 0 53 +0 53 +0 53 +0 53 +0 N N 510 0 53 +1 53 +1 53 +0 53 +2 N N 520 0 53 +inf 53 +inf 53 +0 53 +inf N N 530 0 53 nan 53 nan 53 +0 53 nan N N 540 0 53 +inf 53 -inf 53 +1 53 -inf N N 550 0 53 +1 53 -0 53 +1 53 -0 N N 560 0 53 +1 53 +0 53 +1 53 +0 N N 570 0 53 +inf 53 +inf 53 +1 53 +inf N N 580 0 53 nan 53 nan 53 +1 53 nan N N 590 0 53 +inf 53 -inf 53 +inf 53 -inf N N 600 0 53 +inf 53 -0 53 +inf 53 -1 N N 610 0 53 +inf 53 -0 53 +inf 53 -0 N N 620 0 53 +inf 53 +0 53 +inf 53 +0 N N 630 0 53 +inf 53 +0 53 +inf 53 +1 N N 640 0 53 +inf 53 +inf 53 +inf 53 +inf N N 650 0 53 +inf 53 nan 53 +inf 53 nan N N 660 0 53 +inf 53 -inf 53 nan 53 -inf N N 670 0 53 nan 53 nan 53 nan 53 -1 N N 680 0 53 nan 53 nan 53 nan 53 -0 N N 690 0 53 nan 53 nan 53 nan 53 +0 N N 700 0 53 nan 53 nan 53 nan 53 +1 N N 710 0 53 +inf 53 +inf 53 nan 53 +inf N N 720 0 53 nan 53 nan 53 nan 53 nan N N 73 74# purely real argument 75# sqrt(x +i*0) = sqrt(x) +i*0, when x>0 76# sqrt(x -i*0) = sqrt(x) -i*0, when x>0 77# sqrt(x +i*0) = +0 +i*sqrt(-x) +i*0, when x<0 78# sqrt(x -i*0) = +0 -i*sqrt(-x) +i*0, when x<0 79+ 0 53 0x16a09e667f3bcdp-52 53 +0 53 2 17 +0 N N 800 + 53 +0 53 0x16a09e667f3bcdp-52 54 -2 16 +0 Z N 81+ 0 53 0x16a09e667f3bcdp-52 53 -0 55 2 15 -0 U N 82+ 0 53 0x16a09e667f3bcdp-52 53 -0 55 2 15 -0 A N 830 - 53 +0 53 -0x16a09e667f3bcdp-52 56 -2 14 -0 D N 84- 0 53 0x5a827999fcef30p-54 53 +0 57 2 13 +0 Z Z 850 - 53 +0 53 0x5a827999fcef30p-54 58 -2 12 +0 U Z 86- 0 53 0x5a827999fcef30p-54 53 -0 59 2 11 -0 D Z 870 + 53 +0 53 -0x5a827999fcef30p-54 60 -2 10 -0 N Z 88+ 0 53 0x16a09e667f3bcdp-52 53 +0 61 2 9 +0 U U 89+ 0 53 0x16a09e667f3bcdp-52 53 +0 61 2 9 +0 A A 900 + 53 +0 53 0x16a09e667f3bcdp-52 62 -2 8 +0 D U 910 + 53 +0 53 0x16a09e667f3bcdp-52 62 -2 8 +0 A A 92+ 0 53 0x16a09e667f3bcdp-52 53 -0 63 2 7 -0 N U 93+ 0 53 0x16a09e667f3bcdp-52 53 -0 63 2 7 -0 N A 940 + 53 +0 53 -0x5a827999fcef30p-54 64 -2 6 -0 Z U 95- 0 53 0x5a827999fcef30p-54 53 +0 65 2 5 +0 D D 960 - 53 +0 53 0x5a827999fcef30p-54 66 -2 4 +0 N D 97- 0 53 0x5a827999fcef30p-54 53 -0 67 2 3 -0 Z D 980 - 53 +0 53 -0x16a09e667f3bcdp-52 68 -2 2 -0 U D 990 - 53 +0 53 -0x16a09e667f3bcdp-52 68 -2 2 -0 A A 100 101# purely imaginary argument 102# sqrt(+/-0 +i*y) = sqrt(y/2) * (1 +i), when y >0 103# sqrt(+/-0 +i*y) = sqrt(-y/2) * (1 -i), when y < 0 104+ + 53 0x16a09e667f3bcdp-52 53 0x16a09e667f3bcdp-52 53 +0 53 4 N N 105- + 53 0x5a827999fcef30p-54 53 0x16a09e667f3bcdp-52 51 -0 54 4 Z N 106+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52 49 +0 55 -4 U N 107+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52 49 +0 55 -4 A N 108- - 53 0x5a827999fcef30p-54 53 -0x16a09e667f3bcdp-52 47 -0 56 -4 D N 109- - 53 0x5a827999fcef30p-54 53 0x5a827999fcef30p-54 45 +0 57 4 Z Z 110+ - 53 0x16a09e667f3bcdp-52 53 0x5a827999fcef30p-54 43 -0 58 4 U Z 111+ - 53 0x16a09e667f3bcdp-52 53 0x5a827999fcef30p-54 43 -0 58 4 A Z 112- + 53 0x5a827999fcef30p-54 53 -0x5a827999fcef30p-54 41 +0 59 -4 D Z 113+ + 53 0x16a09e667f3bcdp-52 53 -0x5a827999fcef30p-54 39 -0 60 -4 N Z 114+ + 53 0x16a09e667f3bcdp-52 53 0x16a09e667f3bcdp-52 37 +0 61 4 U U 115+ + 53 0x16a09e667f3bcdp-52 53 0x16a09e667f3bcdp-52 37 +0 61 4 A A 116- + 53 0x5a827999fcef30p-54 53 0x16a09e667f3bcdp-52 35 -0 62 4 D U 117- + 53 0x5a827999fcef30p-54 53 0x16a09e667f3bcdp-52 35 -0 62 4 D A 118+ + 53 0x16a09e667f3bcdp-52 53 -0x5a827999fcef30p-54 33 +0 63 -4 N U 119- + 53 0x5a827999fcef30p-54 53 -0x5a827999fcef30p-54 31 -0 64 -4 Z U 120- - 53 0x5a827999fcef30p-54 53 0x5a827999fcef30p-54 29 +0 65 4 D D 121+ - 53 0x16a09e667f3bcdp-52 53 0x5a827999fcef30p-54 27 -0 66 4 N D 122- - 53 0x5a827999fcef30p-54 53 -0x16a09e667f3bcdp-52 25 +0 67 -4 Z D 123- - 53 0x5a827999fcef30p-54 53 -0x16a09e667f3bcdp-52 25 +0 67 -4 Z A 124+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52 23 -0 68 -4 U D 125+ - 53 0x16a09e667f3bcdp-52 53 -0x16a09e667f3bcdp-52 23 -0 68 -4 A A 126 127# z=(-1.95050937e+25,-2.65087379e-39) 128+ - 24 0x7.2fb038p-164 24 -0x1.011258p32 24 -0x1.0225d4p64 24 -0xe.6ec760p-132 N N 129# z=(-1.89432151e+24,-1.06397210e+09) 130? ? 24 0x0.001954c04p0 24 -0x1.407478p40 24 -0x1.912360p80 24 -0x3.f6aed0p28 N N 131 132# bugs fixed in r160 2008-07-15 133- + 19 0b11101001001001001100p+39 19 -0b1010110101100111011p-236 19 0b1.101010001010100000p+117 19 -0b1.001110111101100001p-158 N Z 134- + 2 0b11p+100 2 -0b11p+100 2 -0 2 -0b11p+203 N Z 1350 + 2 0 2 -0b10p+117 2 -0b11p+235 2 -0 N Z 136 137# close to infinite loop reported by Emmanuel Thome, 22 Oct 2010, 138# and all its variants of signs and directed roundings 139- + 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N 140+ + 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U 141- - 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D 142- + 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D U 143- - 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z 144- - 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N 145+ + 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U 146- - 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D 147- - 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D A 148- + 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z 149+ - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N 150+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U 151+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 A A 152- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 D D 153- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 1 375 -1 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z 154+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 N N 155+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 U U 156+ + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 A Z 157- - 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 -0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z A 158- + 375 0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef5fffffffffffffffffffffffffffffffffffffffffffep-202281177 375 -1 375 -1 375 -0xf.8a8aae3080b3dd665e316d262fd54c1ca22a83dc9acb92ef6p-202281176 Z Z 159